A meaningful expansion around detailed balance (original) (raw)

Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states

Europhysics Letters (epl), 2008

We give the explicit structure of the functional governing the dynamical density and current fluctuations for a mesoscopic system in a nonequilibrium steady state. Its canonical form determines a generalised Onsager-Machlup theory. We assume that the system is described as a Markov jump process satisfying a local detailed balance condition such as typical for stochastic lattice gases and for chemical networks. We identify the entropy current and the traffic between the mesoscopic states as extra terms in the fluctuation functional with respect to the equilibrium dynamics. The density and current fluctuations are coupled in general, except close to equilibrium where their decoupling explains the validity of entropy production principles.

Entropy production in a non-Markovian environment

Physical Review E, 2015

Stochastic thermodynamics and the associated fluctuation relations provide means to extend the fundamental laws of thermodynamics to small scales and systems out of equilibrium. The fluctuating thermodynamic variables are usually treated in the context of isolated Hamiltonian evolution, or Markovian dynamics in open systems. In this work we introduce an explicitly non-Markovian model of dynamics of an open system, where the correlations between the system and the environment drive a subset of the environment outside of equilibrium. This allows us to identify the non-Markovian sources of entropy production. We show that the non-Markovian components lead to modifications in the standard fluctuation relations for entropy. As a concrete example, we explicitly derive such modified fluctuation relations for the case of an overheated single electron box.

Mesoscopic Non-Equilibrium Thermodynamics for the Stochastic Dynamics of Small-Scale Systems

2013

We show how to extend the use of thermodynamic concepts into the mesoscopic domain where fluctuations and nonlinearities play an important role. The theory presented: mesoscopic nonequilibrium thermodynamics, provides a new interpretation of local equilibrium that is formulated at small scales. From it one derives kinetic equations and nonlinear transport equation for the study of small-scale systems outside equilibrium.

Macroscopic fluctuation theory for stationary non-equilibrium states

2002

We formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within this theory we derive the following results: the modification of the Onsager-Machlup theory in the SNS; a general Hamilton-Jacobi equation for the macroscopic entropy; a non equilibrium, non linear fluctuation dissipation relation valid for a wide class of systems; an H theorem for the entropy. We discuss in detail two models of stochastic boundary driven lattice gases: the zero range and the simple exclusion processes. In the first model the invariant measure is explicitly known and we verify the predictions of the general theory. For the one dimensional simple exclusion process, as recently shown by Derrida, Lebowitz, and Speer, it is possible to express the macroscopic entropy in terms of the solution of a non linear ordinary differential equation; by using the Hamilton-Jacobi equation, we obtain a logically independent derivation of this result.

Fluctuations in Stationary Nonequilibrium States of Irreversible Processes

Physical Review Letters, 2001

In this paper we formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which covers situations in a nonlinear hydrodynamic regime and is verified explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Our results include the modification of the Onsager-Machlup theory in the SNS, a general Hamilton-Jacobi equation for the macroscopic entropy and a non equilibrium, non linear fluctuation dissipation relation valid for a wide class of systems. PACS numbers: 05.20.-y, 05.40.-a, 05.60.-k

Mesoscopic non-equilibrium thermodynamics

Basic concepts like energy, heat, and temperature have acquired a precise meaning after the development of thermodynamics. Thermodynamics provides the basis for understanding how heat and work are related and with the general rules that the macroscopic properties of systems at equilibrium follow. Outside equilibrium and away from macroscopic regimes most of those rules cannot be applied directly. In this paper we present recent developments that extend the applicability of thermodynamic concepts deep into mesoscopic and irreversible regimes. We show how the probabilistic interpretation of thermodynamics together with probability conservation laws can be used to obtain kinetic equations describing the evolution of the relevant degrees of freedom. This approach provides a systematic method to obtain the stochastic dynamics of a system directly from the knowledge of its equilibrium properties. A wide variety of situations can be studied in this way, including many that were thought to be out of reach of thermodynamic theories, such as non-linear transport in the presence of potential barriers, activated processes, slow relaxation phenomena, and basic processes in biomolecules, like translocation and stretching.

Mesoscopic thermodynamics of stationary non-equilibrium states

New Journal of Physics, 2005

A thermodynamics for systems at a stationary state is formulated. It is based upon the assumption of the existence of local equilibrium in phase space which enables one to interpret the probability density and its conjugated nonequilibrium chemical potential as mesoscopic thermodynamic variables. The probability current is obtained from the entropy production related to the probability diffusion process and leads to the formulation of the Fokker-Planck equation. For the case of a gas of Brownian particles under steady flow in the dilute and concentrated regimes we derive nonequilibrium equations of state.

Entropy, extropy and information potential in stochastic systems far from equilibrium

Physica A-statistical Mechanics and Its Applications, 2002

The relations between information, entropy and energy, which are well known in equilibrium thermodynamics, are not clear far from equilibrium. Moreover, the usual expression of the classical thermodynamic potentials is only valid near equilibrium. In previous publications, we showed for a chemical system maintained far from equilibrium, that a new thermodynamic potential, the information potential, can be deÿned by using the stochastic formalism of the Master Equation.

Stochastic interacting particle systems out of equilibrium

Journal of Statistical Mechanics: Theory and Experiment, 2007

This paper provides an introduction to some stochastic models of lattice gases out of equilibrium and a discussion of results of various kinds obtained in recent years. Although these models are different in their microscopic features, a unified picture is emerging at the macroscopic level, applicable, in our view, to real phenomena where diffusion is the dominating physical mechanism. We rely mainly on an approach developed by the authors based on the study of dynamical large fluctuations in stationary states of open systems. The outcome of this approach is a theory connecting the non equilibrium thermodynamics to the transport coefficients via a variational principle. This leads ultimately to a functional derivative equation of Hamilton-Jacobi type for the non equilibrium free energy in which local thermodynamic variables are the independent arguments. In the first part of the paper we give a detailed introduction to the microscopic dynamics considered, while the second part, devoted to the macroscopic properties, illustrates many consequences of the Hamilton-Jacobi equation. In both parts several novelties are included.